Question

in the diagram below, \\(\overline{ab} \parallel \overline{cd}\\), \\(\overline{ef} \parallel \overline{gh}\\), and \\(m\angle ikd = 124^\circ\\). find \\(m\angle ajg\\).
step 1: \\(m\angle ikd = 124^\circ\\) (given)
find \\(m\angle ajg = \square^\circ\\) (select a reason)
diagram: lines gh (with h, l, j, g) and ef (with f, k, i, e) are horizontal. lines cd (with c, l, k, d) and ab (with a, j, i, b) are slanting. \\(\angle ikd = 124^\circ\\).

Explanation:

Step1: Find vertical angle of ∠IKD

∠LKF is vertical to ∠IKD, so \( m\angle LKF = 124^\circ \).

Step2: Use parallel lines EF||GH

∠LKF and ∠AJG are corresponding angles (since AB||CD and EF||GH form parallel transversals), so \( m\angle AJG = 124^\circ \).

Answer:

124